<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">d1</font>, <font color="Maroon" title="c3">d2</font>, <font color="Maroon" title="c4">d3</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font>;<br/><b>let </b><font color="Maroon" title="c5">g</font> be   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c1">D</font>;<br/>









<b>assume </b><a NAME="E1:29"/><i><font color="Green" title="E21">A1</font></i>: 
<font color="Maroon" title="c5">g</font> is <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a>
 ;<br/>

<b>thus </b><font color="Maroon" title="c5">g</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c2">d1</font>,<font color="Maroon" title="c3">d2</font>,<font color="Maroon" title="c4">d3</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> = 
<font color="Maroon" title="c5">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c2">d1</font>,<font color="Maroon" title="c3">d2</font></span>)</span>,<font color="Maroon" title="c4">d3</font>
<b>by </b><i><a class="ref" href="finsop_1.html#T15" target="_self" title="FINSOP_1:th.15">Th15</a></i>
<br/>.= 
<font color="Maroon" title="c5">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">d2</font>,<font color="Maroon" title="c2">d1</font></span>)</span>,<font color="Maroon" title="c4">d3</font>
<b>by </b><i><a class="txt" href="finsop_1.html#E1:29"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="binop_1.html#D2" title="BINOP_1:def.2">BINOP_1:def 2</a></i>
<br/>.= 
<font color="Maroon" title="c5">g</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c3">d2</font>,<font color="Maroon" title="c2">d1</font>,<font color="Maroon" title="c4">d3</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finsop_1.html#T15" target="_self" title="FINSOP_1:th.15">Th15</a></i>
;<br/>


</div>
